Liquid crystals, Zeeman relaxation

Jeener and Broekaert introduced, in 1%7, a three-pulse B,(r) sequence to measure the relaxation time Tm of the dipolar order of / = 1 spin systems in the presence of a conventional high Zeeman field, Bq, which is based on the decay time of the so-called Jeener echo . It was later extended by Spiess and Kemp-Harper and Wimperis to study in a similar way the quadrupolar order in / a 1 systems. The appearance of a Jeener echo depends upon the existence of interactions that are not averaged out by molecular motions on the considered time scale. The method has become of great importance in recent relaxation studies, in particular of liquid crystals because, in standard spin relaxation theories, it provides a power l means to separate and analyse the spectral densities / v) and /2) j. i4,is,2025 ggg... 

When relaxation occurs among r.f. pulses, the t dependence in the above sequence provides a means to study spin-lattice relaxation. It is known [2.20] that the Zeeman Tiz) and quadrupole (Tig) spin-lattice relaxation times can be measured for deuterons in liquid crystals from the sum and difference of the doublet signal strengths after the third pulse, respectively. This can be shown using the formalism of rotation operators. The rotation operator R(0, ) provides a general method to describe the effect of a r.f. pulse with rotation angle 0 and phase angle when there are no cyclic commutation relations, such that the simple relation in Eq. (2.60) exists. Now... 

For an isolated spin-1 system, it is convenient to define sum and difference magnetizations [Eqs. (2.84)-(2.85)] in the J-B experiment. The decay of the difference (quadrupolar order) proceeds exponentially at a rate T q, while the sum (Zeeman order) recovers exponentially towards equilibrium at a different rate. The J-B experiment allows simulataneous determination of these rates from which Ji uJo) and J2 2ujo) can be separated. Table 5.1 briefly summarizes thermotropic liquid crystals in which spectral density measurements were reported. Figure 5.4 illustrates the temperature and frequency dependences of spectral densities of motion (in s by including the interaction strength Kq factor) for 5CB-di5. The result is fairly typical for rod-like thermotropic liquid crystals. The spectral densities increase with decreasing temperature in the nematic phase of 5CB. The frequency dependence of Ji uJo) and J2(2a o) indicate that molecular reorientation is likely not in the fast motion regime. However, the observed temperature dependence of the relaxation rates is opposite to what is expected for simple liquids. This must be due to the anisotropic properties (e.g., viscosity) of liquid crystals. 

Relaxation measurements provide another way to study dynamical processes over a large dynamic range in both thermotropic and lyotropic liquid crystals (see Sec. 2.6 of Chap. Ill of Vol. 2A). The two basic relaxation times of a spin system are the spin-lattice or longitudinal relaxation time 7] and the spin-spin or transverse relaxation time T2. A detailed description, however, requires a more precise definition of the relaxation times. For spin 7=1, for instance, two types of spin-lattice relaxation must be distinguished, related to the relaxation of Zeeman and quadrupolar order with rates 7j"2 and Jfg. The relaxation rates depend on spectral density functions which describe the spectrum of fluctuating fields due to molecular motions. A detailed discussion of spin relaxation is beyond the scope of this... 

Cross-relaxation at the nematic-polymer interface. The liquid crystal protons and the polymer protons constitute a two phase proton system. The cross-relaxation at the boundary leads to an exchange of Zeeman energy between the two phases and couples their spin-lattice relaxation rates [202]. Cross-relaxation affects all molecules in the droplet if the exchange of molecules at the surface is so fast that within the spin-lattice relaxation time each molecule in the droplet takes part in this process. For this to take place, both the time required for a molecule to diffuse from the inside of the droplet to the surface Tog, and the time Tg for which the molecules remain anchored at the surface must be short compared to the spin-lattice relaxation time Ty. In the limit of very rapid cross-relaxation (k > (Tf(Tf )p) both phases relax with the same relaxation rate which is an weighted average... 

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